Displacement Errors in Materials Testing
A universal testing machine is used to measure the mechanical properties of materials in tension, compression, bending or torsion. Mechanical properties of interest for plastics in bending are Flexural Strength, Flexural Stress at Break, Tangent, Secant and Chord Modulus of Elasticity. ASTM D790 Flexural Properties of Unreinforced and Reinforced Plastics and Electrical Insulating Materials governs the flexural testing of plastics. In bending, a testing machine is used to create a stress-strain diagram (Figure 1) from which all mechanical properties are derived. A true picture of the stress-strain diagram can only be obtained through accurate measurements.
Figure 1 – ASTM D790 Stress vs. Center Point Deflection curve
Flexural tests on plastics are most often performed with an electromechanical universal testing machine. A schematic of a electromechanical universal testing machine is shown in Figure 2. The testing machine employs a variable speed electric motor, gear reduction system and one, two or four screws to move the crosshead up or down.
Figure 2 – Schematic of an electromechanical universal testing machine
ASTM D790 requires a properly calibrated testing machine that can be operated at constant rates of crosshead motion. The moving crosshead applies force to the test specimen (see Figure 2) at pt 4 equidistant between support pts 1 & 2. According to ASTM D790, the error in force should not exceed +/- 1% of the maximum force expected. For the purposes of measuring flexural strain, the testing machine must also be equipped with a displacement sensor to measure how far the beam deflects at center pt 4. If crosshead motion is used to measure center pt deflection, the total deformation of the testing machine should not exceed 1% of the total deflection of the test specimen. If testing machine deflection exceeds 1%, other means of measuring center pt deflection must be used.
ASTM D790 requires that the test specimen have a rectangular cross section. The specimen rests on two supports and is loaded by means of a loading nose midway between the supports. Figure 2 schematically depicts the ASTM D790 setup. Figure 3 depicts an actual ADMET D790 3 point bend fixture.
Figure 3 – ASTM D790 3-Point Bend Fixture
In Figure 2, the supports and loading nose are shown in light blue. The loading nose contacts the rectangular specimen at pt 4 and is directly connected to the load cell. The test procedure involves deflecting the specimen until rupture occurs in the outer surface of the test specimen or until a maximum strain is reached.
Sensor Location(s) for Measuring Center Point Deflection
The most important consideration in measuring center point deflection is where to mount the deflection sensor. Should the sensor be mounted on the input or output end of the testing machine transmission? If a sensor is mounted on the motor at the input end of the transmission, then the resolution of the system will be enhanced by a factor equal to the transmission ratio. However, backlash and compliance in the transmission, belts, ballscrews, test frame and fixtures will produce measurement errors in the center point deflection. On the other hand, if the sensor is mounted on the output end of the transmission, it will more accurately measure the process but the resolution will be reduced.
Sensor Location Examples for Measuring Center Point Deflection
The test setup shown in Figure 2 has the load cell directly coupled to the loading nose. For purposes of this discussion, we will assume that all force measurements accurately represent the force applied to the specimen and exceed ASTM E4 force accuracy requirements. Representative modulus values will therefore result, if accurate center point deflection values are obtained. Following is a discussion of three sensor location examples. The costs associated with and degree of difficulty employing each example will vary.
Example 1 - Rotary Encoder Mounted on the Motor
Most modern day electromechanical testing machines measure linear crosshead position with a rotary encoder (see Figure 2) mounted to the motor. The motor shaft, right angle transmission, synchronous belt, tapered roller bearings, ballscrew, ballnut, moving crosshead, load cell and loading nose are between the rotary encoder and the test specimen. When a force is applied to the specimen, deflection measurement errors are introduced by the following:
Torsional compliance in the motor shaft due to the applied torque. No machine component is truly rigid, one can think of the motor shaft as a torsion spring with a certain amount of torsional stiffness.
Torsional compliance and mechanical backlash between mating gears in the right angle transmission.
Stretch in the synchronous drive belt.
Compliance in the tapered roller bearings. Tapered roller bearings deform non-linearily, especially at loads which are a fraction of their rating. Preloading the bearings causes a proportionately smaller amount of deflection but may reduce the effective repeatability and resolution of the moving crosshead.
Compliance and lead error in the ballscrews. A compressive load applied to the specimen will create a tensile load in the ballscrews which will cause them to stretch.
Backlash in the ballnuts. When in the unloaded condition, gravity will cause the ball bearings in the ballnuts to be in contact with the upper bearing race. When the applied compressive force exceeds the weight of the moving crosshead, load cell and loading nose, the ball bearings will switch to contacting the lower bearing race.
Compliance in the moving crosshead, load cell, loading nose, specimen supports and machine base. Again, no machine component is truly rigid, one can think of each component as a spring.
As you can see there are many sources of deflection errors when using a rotary encoder mounted to the motor. However, this is the most economical method and the easiest sensor arrangement to employ. If the overall stiffness of the machine is much greater than the stiffness of the specimen, one may be able to use this method for measuring center point deflection.
Example 2 - Linear Displacement Transducer Mounted Between the Moving Crosshead and Top Cross Bracket
A second approach to measuring center point deflection is to install a linear displacement transducer between the top bracket (in green) and the moving crosshead. In Figure 2 it is shown as Displacement B. For this arrangement, when a force is applied to the specimen, strain measurement errors are introduced by the following:
Compliance in the tapered roller bearings.
Compliance in the ballscrews.
Backlash in the ballnuts.
Compliance in the moving crosshead, load cell, loading nose, specimen supports and machine base.
Because the Displacement B transducer is closer than the rotary encoder to the specimen, there are fewer sources of error. The Example 2 method is more accurate and costly than Example 1, but is no more difficult to employ.
Example 3 –Deflectometer Directly Measuring Beam Deflection
When the methods outlined in Examples 1 and 2 are not sufficient to measure center point deflection, a sensor that measures the relative displacement between the underside of the specimen midway between the supports (pt 3 in Figure 2) and the machine base (pt 5) is commonly used. One such device is a deflectometer which is shown in Figure 4. Errors introduced by compliance in the supports and machine base are usually much smaller than the center point deflection values, thus, yielding more accurate center pt deflection measurements. Example 3 costs are greater than 1 and 2 and is somewhat more difficult to employ because the deflectometer is located in the same space as the specimen and will require more handling.
Figure 4 - A deflectometer mounted on a magnetic base
All experimental measurements include errors. Before commencing testing, always ask the question: “Are my measurement errors small enough to not matter?” A thorough understanding of the sources and magnitudes of the errors is paramount to making accurate measurements.